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%I #19 Sep 08 2022 08:44:57
%S 0,0,0,0,0,0,2,12,18,63,168,224,504,1014,1270,2420,4620,5742,12012,
%T 27027,35035,84119,199304,260064,601664,1339464,1720944,3755844,
%U 8093214,10329750,22591800,49876200,64071194,144780009
%N Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= n/3.
%H Robert Israel, <a href="/A048001/b048001.txt">Table of n, a(n) for n = 1..3633</a>
%F a(n) = Sum_{k=1..ceiling(2*n/3)/5} binomial(floor(n/3),k)*binomial(ceiling(2*n/3),5*k). - _Robert Israel_, Nov 12 2018
%p f:= proc(n) local n3, k;
%p n3:= floor(n/3);
%p add(binomial(n3,k)*binomial(n-n3,5*k),k=1..(n-n3)/5);
%p end proc:
%p map(f, [$1..50]); # _Robert Israel_, Nov 11 2018
%t Table[Sum[Binomial[Floor[n/3],k]*Binomial[n-Floor[n/3], 5*k], {k,1, n-Floor[n/3]}], {n,1,40}] (* _G. C. Greubel_, Nov 11 2018 *)
%o (PARI) vector(40, n, sum(k=1, n-n\3, binomial(n\3,k)*binomial(n - n\3, 5*k))) \\ _G. C. Greubel_, Nov 11 2018
%o (Magma) [(&+[Binomial(Floor(n/3), k)*Binomial(n - Floor(n/3), 5*k): k in [1..(n - Floor(n/3))]]): n in [1..40]]; // _G. C. Greubel_, Nov 11 2018
%K nonn
%O 1,7
%A _Clark Kimberling_
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